carrier. Therefore when you see a diagram of an
FM algorithm, the carriers are always on the
bottom row and the modulators are stacked above
the carrier. Each carrier is audible directly, while
each modulator influences the timbre of the
operator beneath it. Stacks can become quite
complex, but only those operators on the bottom
of the algorithm chart are audible directly. You
can stack modulator on top of modulator and get
very complex tones – as you will hear from this
set. Operators can even modulate themselves
(called a feedback loop) and since output can be
controlled by velocity and other controllers you
have a degree of control over harmonic content
that samples can’t even dream about. So while
samples offer a very accurate wave shape to
start, your ability to manipulate on an organic
level is nil. FM wave shapes are not as emulative
of instruments to start but the behavior and
degree of control over harmonic content is
unprecedented.
In the algorithm above operators 1, 3, 4 and 5 are
Carriers (meaning you can hear their output)
while operators 2 and 6 are Modulators (means
their output is only heard by its affect on the
Carriers to which they are connected. Without the
Modulators each Carrier would sound only a ‘sine
wave’. Operator 6, above, is the feedback
operator (where the signal can get very complex
as it is fed back on itself – generating complex
sidebands).
When you have a simple 2-operator FM stack,
(like operator’s 2 and 1 above) Modulator/Carrier,
and the coarse tuning ratio of each is 1.00 and
the output of the modulator is about at ¾ output
(about 75), you will generate a fairly perfect
sawtooth waveform, 1:1. If you increase the ratio
of the modulator frequency so that it is 2:1 tuning
ratio to the carrier you will generate a square
wave. Any whole integer ratio 3:1, 4:1, 5:1 or
greater will generate an ever-narrowing pulse
wave. If the ratio is a non-whole integer
relationship, you will generate what would be
described as a ‘bell tone’. That is the
fundamentals of FM – of course, it can get very
much more complex (FM is a real form a
synthesis that can be studied at the college level),
with nested feedback loops and interaction
between operators. Filters were unnecessary in
the original FM synthesizer since you were
constructing the harmonic content more directly.
To really get into FM you need to understand side-
band frequencies and Bessel functions but most
FM synthesis can be carried out on an intuitive
basis once you understand the fundamentals.
If none of this interests you, it is okay. You can
just enjoy the sounds. But without much
exaggeration I can say that most of what is
possible with DX-style FM has yet to be explored.
And there are sounds that nothing but DX-style
FM can do. Notice I didn’t say it could do
everything – but there are sounds that nothing
else on the planet can do. It is estimated that
there are some 10,000 useable FM sounds out
there floating around. Some people insist they can
“sample” it – you can’t. Well, of course, you can,
but what you miss is the interaction of the
modulator and carrier within the sound. Each
operator has its own envelope, its own response
to velocity, etc. – this makes what happens within
the FM voice a ‘living’ thing – it is more organic
than can be captured in a simple sample of a
waveform. Envelopes and output indexes can be
influenced on a continuous basis, which in turn
changes the timbre of the sound as you increase
playing intensity – this is what cannot be
sampled. The tremendous success of the DX7
‘back-in-the-day’ was not based on anything more
than musicians thought that the sound was ‘cool’.
Most DX7 owners never programmed an FM Voice
– the least pressed button in the world was the
EDIT button on a DX7. It was way too complicated
– but a good lesson was learned here –
complexity comes in a paltry second to SOUND
when musician’s make up their mind they like
something. (Well, duh, most sax players don’t
have a clue about how a saxophone makes sound
and would be hard pressed to discuss Bernoulli’s
principle and the Graham Non-linear curve, and
just what is hysteresis and the fricative value and
what does it have to do with saxophone tone?)
However, if you want to get involved with
programming and tweaking FM – you will find
your results their own reward. There is an
excellent tutorial on-line at the Yamaha Digital
Music World site – with a number of lessons
taking you through the world of sine waves and
operators – and the first ‘synthesizers’.
Visit the FM Tone Generator Seminar at:
http://www.digitalmusicworld.com/html/hardw
are/SynthsTutorial.asp
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